“Minimax length links” of a dissimilarity matrix and minimum spanning trees

A theorem is proved stating that the set of all minimax links, defined as links minimizing, over paths, the maximum length of links in any path connecting a pair of objects comprising nodes in an undirected weighted graph, comprise the union of all minimum spanning trees of that graph. This theorem is related to methods of fitting network models to dissimilarity data, particularly a method called Pathfinder due to Schvaneveldt and his colleagues, as well as to single linkage clustering, and results concerning the relationship between minimum spanning trees and single linkage hierarchical trees.Acknowledgments: The author thanks Phipps Arabie, Lawrence J. Hubert, and K. Christoph Klauer for a number of helpful suggestions and comments on various aspects of this paper.     

Wittgenstein and the <Emphasis Type="Italic">Xunzi</Emphasis> on the Clarification of Language

Broadly speaking, language is part of a social activity in both Wittgenstein and Xunzi 荀子, and for both clarification of language is central to their philosophical projects; the goal of this article is to explore the extent of resonance and discord that may be found when comparing these two philosophers. While for Xunzi, the rectification of names (zhengming 正名) is anchored in a regard for establishing, propagating, and/or restoring a harmonious social system, perspicuity is for Wittgenstein represented as a philosophical end in itself. The article ventures study in particular the themes of perspicuity and aspect-perception in Wittgenstein together with the topics of correcting names and the cultivation of the heart-mind (xin 心) in the Xunzi. The aspiration of this project is to gain an overview of the role(s) of clarification projects in different philosophical traditions, all while not overlooking the different historical contexts and philosophical ends of these two philosophers.     

Timing dysfunctions in schizophrenia as measured by a repetitive finger tapping task

Schizophrenia may be associated with a fundamental disturbance in the temporal coordination of information processing in the brain, leading to classic symptoms of schizophrenia such as thought disorder and disorganized and contextually inappropriate behavior. Although a variety of behavioral studies have provided strong evidence for perceptual timing deficits in schizophrenia, no study to date has directly examined overt temporal performance in schizophrenia using a task that differentially engages perceptual and motor-based timing processes. The present study aimed to isolate perceptual and motor-based temporal performance in individuals diagnosed with schizophrenia using a repetitive finger-tapping task that has previously been shown to differentially engage brain regions associated with perceptual and motor-related timing behavior. Thirty-two individuals with schizophrenia and 31 non-psychiatric control participants completed the repetitive finger-tapping task, which required participants to first tap in time with computer-generated tones separated by a fixed intertone interval (tone-paced tapping), after which the tones were discontinued and participants were required to continue tapping at the established pace (self-paced tapping). Participants with schizophrenia displayed significantly faster tapping rates for both tone- and self-paced portions of the task compared to the non-psychiatric group. Individuals diagnosed with schizophrenia also displayed greater tapping variability during both tone- and self-paced portions of the task. The application of a mathematical timing model further indicated that group differences were primarily attributable to increased timing – as opposed to task implementation – difficulties in the schizophrenia group, which is noteworthy given the broad range of impairments typically associated with the disorder. These findings support the contention that schizophrenia is associated with a broad range of timing difficulties, including those associated with time perception as well as time production.     

Machine short-cuts in the computation of chisquare and the contingency coefficient

Rapid computational routines are presented for calculatingx ² from frequency data in the following cases: (1) test of goodness of fit between an observed and a theoretical distribution; (2) test of independence of distributions displayed in anr ×c table; (3) test of independence of distributions displayed in anr × 2 table. A rapid method of computing the contingency coefficient also follows from the procedure used in the second of these cases.